The twentieth century has witnessed an unprecedented "crisis in the foundations of mathematics", featuring a world-famous paradox (Russell"s Paradox), a challenge to "classical" mathematics from a world-famous mathematician (the "mathematical intuitionism" of Brouwer), a new foundational school (Hilbert"s Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of "mathematical philosophy", associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.